By Sam Alex, civil engineer · About the author
Percentages are everywhere: pay rises, sales, interest rates, GST, news headlines. Most errors come from a handful of traps. Here they are, with worked examples.
The one formula behind most of it
Part ÷ whole × 100. If 18 of 24 people agree, that's 18 ÷ 24 × 100 = 75%. The percentage calculator does this, and the percentage change calculator handles "from A to B" questions.
Trap 1: stacked discounts
"20% off, plus an extra 10% at the checkout" sounds like 30%. It isn't: 1. $200 less 20% = $160 2. $160 less 10% = $144 3. Total saving: $56, which is 28%
Each discount applies to the price after the previous one. The discount calculator lets you check each step.
Trap 2: up then down isn't back to even
A price rises 10% from $100 to $110, then falls 10%: $110 − $11 = $99. Losses and gains aren't symmetrical because each one is a percentage of a different starting figure. Investments work the same way: a 50% fall needs a 100% gain to recover.
Trap 3: taking GST off a price
In Australia, GST is 10% of the price before tax. So the GST inside a GST-inclusive price is one-eleventh of it, not 10%: - $275 including GST ÷ 11 = $25 GST, so the price before GST is $250 - Taking 10% off $275 gives $247.50, which is wrong
Adding GST is easier: multiply by 1.1. The GST calculator does both.
Trap 4: pay rises versus inflation
You get a 3% pay rise, but prices rose 3.5% over the same year. Your real pay has fallen by about 0.5%: 1.03 ÷ 1.035 = 0.995. That's why pay rises are often compared with the Consumer Price Index (CPI) that the ABS publishes each quarter.
On a $70,000 salary, a 3% rise is $2,100 a year before tax, or about $40 a week before tax.
Trap 5: percent vs percentage points
If the cash rate goes from 4.10% to 4.35%, it rose by 0.25 percentage points, but by 6.1% in relative terms. News reports sometimes say "rates rose 0.25%", which is technically ambiguous. For your mortgage, the percentage-point figure is what matters: on a $600,000 loan over 30 years, each 0.25-point rise adds roughly $95–100 a month.
Trap 6: margin versus markup
A shop buys an item for $60 and sells it for $100: - Markup (profit ÷ cost) = 40 ÷ 60 = 66.7% - Margin (profit ÷ price) = 40 ÷ 100 = 40%
Businesses that add a "40% markup" expecting a 40% margin are underpricing. The profit margin calculator explains the difference.
Quick mental shortcuts
- 10%: move the decimal point one place (10% of $86 = $8.60)
- 5%: half of 10%
- 15%: 10% plus 5%
- 25%: divide by 4
- X% of Y = Y% of X: 4% of 75 is the same as 75% of 4, which is 3
Frequently asked questions
How do I calculate a percentage increase?
(New − old) ÷ old × 100. From $480 to $520 is an 8.3% increase.
How do I remove GST from a price?
Divide the GST-inclusive price by 11 to find the GST, then subtract it. $110 includes $10 GST.
Is 20% off then 10% off the same as 30% off?
No. It's 28% off, because the second discount applies to the reduced price.